The present invention relates, in general, to computer graphics processing, operator interface processing, and selective visual display systems and, in particular, to waveform display (e.g., oscilloscope type).
Signals are often described as complex numbers. A complex number is a number in the form of a+bi, where a and b are real numbers, and where i is the square root of xe2x88x921. The first part of the complex number (i.e., a) is referred to as the real component, and the second part of the complex number (i.e., bi) is referred to as the imaginary component. The magnitude and phase of a signal are each derived from both the real and imaginary components of the complex number that represents the signal. The equations for finding the magnitude and phase of a signal described by a complex number may be found on page 39 of a 1995 book by Robert W. Ramirez, entitled xe2x80x9cThe FFT Fundamentals and Concepts.xe2x80x9d The magnitude of such a signal may be found by squaring the real component, squaring the imaginary component, summing the two squared terms, and finding the square root of the sum. The result of the square root is the magnitude. The phase is found by dividing the imaginary component by the real component and finding the inverse tangent of the quotient. The result of the inverse tangent is the phase. As you can see, both the real component and the imaginary component contribute to both the magnitude and the phase of the signal. Typical oscilloscopes display the magnitude or phase of a signal versus time, but not the real and imaginary components separately. By combining the real and imaginary components of a waveform on a single axis, the user is forced to mentally integrate the real and imaginary components from the combined information to get a sense of how the complex waveform evolves over time.
Where the phase of a signal is plotted versus time, the range of the phase is often artificially restrained to +/xe2x88x92180 degrees. Such a restriction complicates the phase depiction near these limits by causing abrupt shifts from +180 degrees to xe2x88x92180 degrees or vice versa. Such a distortion does not give the user a true sense of the phase history at these limits.
U.S. Pat. No. 5,739,807, entitled xe2x80x9cMETHOD FOR PRESENTING COMPLEX NUMBER WAVEFORMS,xe2x80x9d displays a complex waveform by (1) graphing the magnitude of the signal versus time while representing the phase of the signal by color or area under the curve or (2) graphing the phase of the signal versus time while representing the magnitude of the signal by color or area under the curve. To separate the real component from the imaginary component, a user must integrate the two different display forms of U.S. Pat. No. 5,739,807. Also, U.S. Pat. No. 5,739,807 does not disclose a method of displaying a signal represented by a complex number where the real and imaginary components are displayed separately as does the present invention. U.S. Pat. No. 5,739,807 is hereby incorporated by reference into the specification of the present invention.
Plotting a single set of the real and imaginary components is disclosed on page 76-77 of a book entitled xe2x80x9cThe Prentice Hall Encyclopedia of Mathematics which was published in 1982. However, this book does not disclose a method of displaying numerous sets of such plots with additional display features as does the present invention.
It is an object of the present invention to obtain a time history of a signal without having to integrate information on magnitude versus time and phase versus time.
It is another object of the present invention to obtain a time history of a signal by separately displaying sets of the real and imaginary components of a signal versus time.
The present invention is a method of obtaining a time history of a signal without having to integrate information on magnitude versus time and phase versus time by separately displaying sets of the real and imaginary components of a signal verses time.
The first step of the method is sampling a signal in time.
The second step of the method is selecting a user-definable size of a display.
The third step of the method is determining the real and imaginary components for each time sample of the signal.
The fourth step of the method is selecting a user-definable number of samples to be displayed at any one instance.
The fifth step of the method is displaying each sample to be displayed according to its real component along the X-axis, the imaginary component along the Y-axis, and the time associated with the sample along the Z-axis.